952
18–41.
The spool has a mass of 20 kg and a radius of gyration of
kO=160 mm
. If the 15-kg block A is released from rest,
determine the distance the block must fall in order for the
spool to have an angular velocity v
=8 rad>s
. Also, what is
the tension in the cord while the block is in motion? Neglect
the mass of the cord.
SOLUTION
sb=0.2418 m =242 mm
200 mm
O
953
18–42.
The spool has a mass of 20 kg and a radius of gyration of
kO=160 mm
. If the 15-kg block A is released from rest,
determine the velocity of the block when it descends
600mm.
SOLUTION
200 mm
O
954
18–43.
SOLUTION
10 ft
u
A
un
if
orm
l
a
dd
er
h
av
i
ng a we
i
g
h
t o
f
30
lb
i
s re
l
ease
d
f
rom
rest when it is in the vertical position. If it is allowed to fall
freely, determine the angle u at which the bottom end A
starts to slide to the right of A.For the calculation, assume
the ladder to be a slender rod and neglect friction at A.
955
*18–44.
AB
C
150 mm
100 mm
200 mm
Determine the speed of the 50-kg cylinder after it has
descended a distance of 2 m, starting from rest. Gear Ahas
a mass of 10 kg and a radius of gyration of 125 mm about its
center of mass. Gear Band drum Chave a combined mass
of 30 kg and a radius of gyration about their center of mass
of 150 mm.
956
18–45.
The 12-kg slender rod is attached to a spring, which has an
unstretched length of 2 m. If the rod is released from rest
when
u=30°
, determine its angular velocity at the instant
u=90°
.
SOLUTION
2 m
u
2 m
A
C
k 40 N/m
B
957
18–46.
The 12-kg slender rod is attached to a spring, which has an
unstretched length of 2 m. If the rod is released from rest
when
u=30°
, determine the angular velocity of the rod the
instant the spring becomes unstretched.
SOLUTION
2 m
u
2 m
A
C
k 40 N/m
B
958
18–47.
The 40-kg wheel has a radius of gyration about its center of
gravity G of
kG=250 mm
. If it rolls without slipping,
determine its angular velocity when it has rotated clockwise
90° from the position shown. The spring AB has a stiffness
k=100 N>m
and an unstretched length of 500 mm. The
wheel is released from rest.
SOLUTION
G
B
A
k 100 N/m
1500 mm
400 mm
200 mm
200 mm
959
18–48.
The assembly consists of two 10-kg bars which are pin
connected. If the bars are released from rest when
u=60°
,
determine their angular velocities at the instant
u=0°
. The
5-kg disk at C has a radius of 0.5 m and rolls without slipping.
A
3 m3 m
C
B
uu
SOLUTION
960
18–49.
The assembly consists of two 10-kg bars which are pin
connected. If the bars are released from rest when
u=60°
, determine their angular velocities at the instant
u=30°
. The 5-kg disk at C has a radius of 0.5 m and rolls
without slipping. A
3 m3 m
C
B
uu
SOLUTION
961
18–49. Continued
962
18–50.
SOLUTION
The compound disk pulley consists of a hub and attached
outer rim. If it has a mass of 3 kg and a radius of gyration
determine the speed of block Aafter A
descends 0.2 m from rest. Blocks Aand Beach have a mass
of 2 kg. Neglect the mass of the cords.
kG=45 mm,
100 mm
30 mm
Ans:
vA=1.40 m>s
963
18–51.
The uniform garage door has a mass of 150 kg and is guided
a
long smooth tracks at its ends.Lifting is done using the two
springs
,each of which is attached to the anchor bracket at A
and
to the counterbalance shaft at Band C.As the door is
raised,
the springs begin to unwind from the shaft, thereby
a
ssisting the lift. If each spring provides a torsional moment of
,where is in radians,determine the angle
at which both the left-wound and right-wound spring
should be attached so that the door is completely balanced by
the springs
,i.e., when the door is in the vertical position and is
g
iven a slight force upwards,the springs will lift the door along
the
side tracks to the horizontal plane with no final angular
velocity
.Note: The elastic potential energy of a torsional
spring
is ,where and in this case
.
k
=0.7 N #m>rad
M=kuV
e=1
2ku2
u
0
u
M
=(0.7u)N
#m
SOLUTION
3m 4m
C
A
B
964
*18–52.
The two 12-kg slender rods are pin connected and released
from rest at the position
u=60°
. If the spring has an
unstretched length of 1.5 m, determine the angular velocity
of rod BC, when the system is at the position
u=0°
. Neglect
the mass of the roller at C.
A
C
B
2 m
k 20 N/m
2 m
u
SOLUTION
965
18–52. Continued
Ans:
(
v
BC)2=3.00 rad>s
966
18–53.
The two 12-kg slender rods are pin connected and released
from rest at the position
u=60°
. If the spring has an
unstretched length of 1.5 m, determine the angular velocity
of rod BC, when the system is at the position
u=30°
.
SOLUTION
A
C
B
2 m
k 20 N/m
2 m
u
967
18–53. Continued
Ans:
vBC
=1.34 rad>s
968
18–54.
k 75 lb/ft
0.75 ft
0.375 ft
O
If the 250-lb block is released from rest when the spring is
unstretched, determine the velocity of the block after it has
descended 5 ft. The drum has a weight of 50 lb and a radius
of gyration of about its center of mass O.kO=0.5 ft
SOLUTION
Ans:
vb=15.5 ft>s